1、HydraulicConsiderations For CorrugatedPolyethylene Pipe Brought to you by the CPPA, a non-profit industry trade association dedicated to providing unbiased, non-brandedinformation about the use andinstallation of corrugated polyethylene pipe.Your Information ResourceHydraulicsCORRUGATEDPOLYETHYLENEP
2、IPEASS O CIATIONAC P PA division of the Plastics Pipe Institute, Inc.TMPrefaceThe material presented in this technical booklet has been prepared in accordance with recognized principles and practices, and is for general information only. The informationshould not be used without first securing compe
3、tent advice with respect to its suitability for any general or specific application.While the material is believed to be technically correct, the Corrugated Polyethylene PipeAssociation makes no representation or warranty of any kind, and assumes no liability therefore. Inquiries on specific product
4、s, their attributes, and the manufacturers warrantyshould be directed to member companies. An up-to-date directory of the membership of the Corrugated Polyethylene Pipe Association is available on request.Table of ContentsIntroduction 4Overview of Hydraulic Considerations 5Discharge Curves 6Conveyan
5、ce Method 8Self-Cleansing Velocities 12Value Considerations 14Example Problems 16Footnotes 19Corrugated polyethylene drainage pipe is available in single wall (corrugated interior), anddual wall (smooth interior), designs. Dual wall corrugated polyethylene pipe is designed witha strong corrugated ou
6、ter wall and a smooth interior wall to improve long-term hydraulic efficiency. In fact, this type of corrugated polyethylene stormwater drainage pipe offers up to 50% more capacity than comparably sized corrugated steel and significantly more capacitythan reinforced concrete pipe. Smooth interior pi
7、pe wont snag debris or encourage sediment, even on shallow grades, and these superior hydraulics allow pipe systems to be downsized compared to traditionalmaterials, reducing material and labor costs.Introduction4The actual sizing of drainage pipes can be a tedious process. Fortunately, simplificati
8、on procedures are available to make pipe selection faster and easier. The material in the following sections provides two methods both based on the Mannings formula whichsimplify the corrugated polyethylene pipe selection process.Discharge curves provide one way to size pipe. Graphs are utilized onc
9、e the design capacityrequirements and slope have been established. Each corrugated polyethylene pipe producthas its own discharge curve based on its Mannings “n” value.Another method of sizing pipe involves conveyance factors and allows the designer to develop product options easily. Use of this met
10、hod frequently results in more than one satisfactory pipe type and size for a given drainage need, thereby revealing the most cost-effective solution.Final pipe selection also should include a review of the velocity conditions. Higher flowvelocities help keep sediment in stormwater from settling alo
11、ng the bottom of the smoothinterior corrugated polyethylene pipe. A reduction in sediment can also reduce maintenancerequirements and help ensure the hydraulic function of the pipe continues throughout itsdesign life.Overview of Hydraulic Considerations5The mathematical relationship of the terms inc
12、luded in the Mannings formula is oftenshown graphically through discharge curves. The curves aid in the sizing of pipe once the required capacity and slope have been determined.Discharge curves for two types of polyethylene pipe are shown in Figures 1 and 2.Figure 1: Discharge Rates for Corrugated P
13、olyethylene Pipe With a Smooth Interior (assumes n = 0.010)6Discharge Curves100908070605040302010987654321.00.90.80.70.60.50.40.30.20.12.82.52.32.01.71.41.10.850.570.280.250.230.200.170.140.110.0850.0570.0280.0250.0230.0200.0170.0140.0110.00850.00570.0028Pipe Slope (%)Flow Capacity (cfs)Flow Capacit
14、y (m3/s)0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.010.060“ (1500mm)54“ (1350mm)48“ (1200mm)42“ (1050mm)36“ (900mm)30“ (750mm)24“ (600mm)21“ (525mm)18“ (450mm)15“ (375mm)12“ (300mm)10“ (250mm)8“ (200mm)6“ (150mm)4“ (100mm)10fps (
15、3.0m/s)9fps (2.7m/s)8fps (2.4m/s)7fps (2.1m/s)6fps (1.8m/s)5fps (1.5m/s)4fps (1.2m/s)3fps (0.9m/s)2fps (0.6m/s)1fps (0.3m/s)Note: Actual “n” values may vary at the engineers discretion. Solid lines indicate pipe diameter.Dashed lines indicate approximate flow velocity.Figure 2: Discharge Rates for C
16、orrugated Polyethylene Pipe With a Corrugated Interior7100908070605040302010987654321.00.90.80.70.60.50.40.30.20.12.82.52.32.01.71.41.10.850.570.280.250.230.200.170.140.110.0850.0570.0280.0250.0230.0200.0170.0140.0110.00850.00560.0028Pipe Slope (%)Flow Capacity (cfs)Flow Capacity (m3/s)0.01 0.02 0.0
17、3 0.04 0.05 0.06 0.07 0.08 0.090.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.010.024“ (600mm)18“ (450mm)15“ (375mm)12“ (300mm)10“ (250mm)8“ (200mm)6“ (150mm)4“ (100mm)3“ (75mm)10fps (3.0m/s)9fps (2.7m/s)8fps (2.4m/s)7fps (2.1m/s)6fps (1.8m/s)5fps (1.5m/s)4fps (1.2m/s)3fps (0.
18、9m/s)2fps (0.6m/s)1fps (0.3m/s)Note: The “n” value changes from diameter to diameter for corrugated interior pipe because of differences in corrugation geometry. (4“ - 6“: 0.015; 8“: 0.016; 10: 0.017: 12“ - 15“: 0.018; 18“ - 24“: 0.020)1Solid lines indicate pipe diameter.Dashed lines indicate approx
19、imate flow velocity.Conveyance MethodConveyance provides a convenient means of selecting a variety of pipe options to satisfy a projects flow requirements. Conveyance factors are based on a greatly simplified version of the Mannings equation shown in Equation 1 or 1(a) with metric units.Equation 1Q
20、= 1.486 AR2/3S1/2nWhere:Q = pipe capacity, cfsn = Mannings “n” (unitless), a term used to describe material roughness A = cross-sectional flow area of the pipe (ft2) R = hydraulic radius (ft), 1/4 the diameter for full-flowing pipe conditionsS = pipe slope (feet/foot)Equation 1(a)Q = AR2/3 S1/2nWher
21、e:Q = pipe capacity (m3/s)n = Manning “n” (unitless)A = cross sectional flow area of the pipe (m2)R = hydraulic radius (m), 1/4 the diameter for full-flowing pipe conditionsS = pipe slope (meter/meter)For a specific full-flowing pipe installation, the parameters n, A, and R are easily defined consta
22、nts. The flow-carrying ability, or conveyance factor, of the pipe can then be defined as shown in Equation 2 or 2(a) with metric units.Equation 2k = 1.486 AR2/3nWhere:k = conveyance factor8Equation 2(a)k = AR2/3nBy substitution, the Mannings formula can then be reduced to the following equation.Equa
23、tion 3Q = kS1/2Equation 3 also can be written as shown in Equation 4.Equation 4k = Q S1/2Direct substitution of design conditions into Equation 4 will determine the minimum conveyance factor allowed. Use Table 1 or Table 1(a) for metric equivalent as a guide to selecting a corrugated polyethylene pi
24、pe having a conveyance factor of at least what youve calculated.The Mannings “n” is a critical value in the conveyance concept. Among pipes of the samediameter, the Mannings “n” is the only factor that has an effect on conveyance and, therefore,capacity. When comparing identical field conditions, co
25、nveyance has a direct relationship tocapacity. This means that if the slope is held constant, tripling conveyance will triple the capacity and halving conveyance will halve the capacity.Problems involving conveyance factors are explained in the Example Problems sectionon page 16.9Table 1: Conveyance
26、 Factors for Corrugated Polyethylene Pipe (English Units)10Dia.AreaManning Value(in.)(sq. ft.)0.0090.0100.0110.0120.0130.0140.0150.0160.0170.0180.0190.0200.0210.0220.0230.024 0.02530.051.31.11.01.00.90.80.80.70.70.60.60.60.50.50.50.50.540.092.72.52.22.11.91.81.61.51.51.41.31.21.21.11.11.01.060.208.1
27、7.36.66.15.65.24.94.64.34.13.83.63.53.33.23.02.980.3517.515.714.313.112.111.210.59.89.28.78.37.97.57.16.86.56.3100.5531.628.525.923.721.920.319.017.816.815.815.014.213.612.912.411.911.4120.7951.546.342.138.635.633.130.928.927.225.724.423.222.121.120.119.318.5151.2393.384.076.370.064.660.056.052.549.
28、446.744.242.040.038.236.535.033.6181.77151.7136.6124.1113.8105.097.591.085.380.375.971.968.365.062.159.456.954.6212.41228.9206.0187.3171.6158.4147.1137.3128.7121.2114.4108.4103.098.193.689.685.882.4243.14326.8294.1267.3245.1226.2210.1196.1183.8173.0163.4154.8147.0140.0133.7127.9122.5117.6273.98447.3
29、402.6366.0335.5309.7287.6268.4251.6236.8223.7211.9201.3191.7183.0175.0167.8161.0304.91592.5533.2484.7444.3410.2380.9355.5333.3313.7296.2280.6266.6253.9242.4231.8222.2213.3335.94763.9687.5625.0572.9528.9491.1458.3429.7404.4382.0361.9343.8327.4312.5298.9286.5275.0367.07963.4867.1788.2722.6667.0619.357
30、8.0541.9510.0481.7456.4433.5412.9394.1377.0361.3346.8429.621453.21307.91189.01089.91006.1934.2871.9817.5769.4726.6688.4654.0622.8594.5568.7545.0523.24511.041746.81572.11429.21310.11209.31122.91048.1982.6924.8873.4827.4786.1748.6714.6683.5655.0628.84812.572074.81867.41697.61556.11436.41333.81244.9116
31、7.11098.41037.4982.8933.7889.2848.8811.9778.1746.95415.902840.52556.42324.02130.41966.51826.01704.31597.81503.81420.21345.51278.21217.41162.01111.51065.21022.66019.633762.03385.83078.02821.52604.42418.42257.22116.11991.61881.01782.01692.91612.31539.01472.11410.71354.3Design Mannings Values* for Corr
32、ugated Polyethylene Pipe *Mannings coefficient for smooth interior pipe determined at Utah State University Water Research Laboratory.Conveyance Equations: k= Q/S1/2or Q = kS1/2Note: Highlighted columns are representative of smooth interior polyethylene pipe.ProductDiameterMannings “n”Typical Smooth
33、 Interior4“ 60“ 0.010 - 0.012Typical Corrugated Interior3“ 6“ 0.0158“ 0.01610“0.01712“ 15“0.01818“ 24“ 0.02011Dia.AreaManning Value(mm)(sq. m)0.0090.0100.0110.0120.0130.0140.0150.0160.0170.0180.0190.0200.0210.0220.0230.0240.025750.0040.030.030.030.030.020.020.020.020.020.020.020.020.010.010.010.010.
34、011000.0080.070.070.060.060.050.050.040.040.040.040.040.030.030.030.030.030.031500.0180.220.200.180.160.150.140.130.120.120.110.100.100.090.090.090.080.082000.0310.470.430.390.360.330.300.280.270.250.240.220.210.200.190.190.180.172500.0490.860.770.700.640.590.550.520.480.450.430.410.390.370.350.340.
35、320.313000.0711.401.261.141.050.970.900.840.790.740.700.660.630.600.570.550.520.503750.1102.532.282.071.901.751.631.521.421.341.271.201.141.091.040.990.950.914500.1594.123.713.373.092.852.652.472.322.182.061.951.851.761.681.611.541.485250.2166.215.595.084.664.303.993.733.493.293.112.942.802.662.542.
36、432.332.246000.2838.877.987.266.656.145.705.324.994.704.434.203.993.803.633.473.333.196750.35812.1410.939.939.118.417.807.286.836.436.075.755.465.204.974.754.554.377500.44216.0814.4713.1612.0611.1310.349.659.048.518.047.627.246.896.586.296.035.798250.53520.7318.6616.9615.5514.3513.3312.4411.6610.981
37、0.379.829.338.898.488.117.777.469000.63626.1523.5321.3919.6118.1016.8115.6914.7113.8413.0712.3911.7711.2110.7010.239.819.4110500.86639.4435.5032.2729.5827.3125.3623.6722.1920.8819.7218.6817.7516.9016.1415.4314.7914.2011250.99447.4142.6738.7935.5632.8230.4828.4526.6725.1023.7022.4621.3320.3219.3918.5
38、517.7817.0712001.13156.3150.6846.0742.2338.9936.2033.7931.6829.8128.1626.6725.3424.1323.0422.0421.1220.2713501.43177.0969.3863.0857.8253.3749.5646.2643.3640.8138.5536.5234.6933.0431.5430.1728.9127.7515001.767102.1091.8983.5476.5870.6965.6461.2657.4354.0551.0548.3645.9543.7641.7739.9538.2936.76Table
39、1(a) : Conveyance Factors for Corrugated Polyethylene Pipe (Metric Units)Design Mannings Values* for Corrugated Polyethylene Pipe *Mannings coefficient for smooth interior pipe determined at Utah State University Water Research Laboratory.Conveyance Equations: k= Q/S1/2or Q = kS1/2Note: Highlighted
40、columns are representative of smooth interior polyethylene pipe.ProductDiameterMannings “n”Typical Smooth Interior100 - 1500 mm0.010 - 0.012Typical Corrugated Interior75 - 150 mm0.015200 mm0.016250 mm0.017300 - 375 mm0.018450 - 600 mm0.020Sediment can reduce the capacity of a stormwater pipe over ti
41、me. In some installations, it may render the pipe useless until the system can be cleaned. This is an expensive, time-consuming undertaking, so preventive measures should be taken during design.Sedimentation is of great concern in storm sewer application, because large, heavy grit may be present. To
42、 minimize potential problems, flow should be maintained at a minimum, or self-cleansing, velocity.Flow velocity can be increased by either increasing the slope of the pipe or by using a smaller diameter. Modifying either the slope or pipe size requires careful consideration of site factors and flow
43、needs. However, by using a corrugated polyethylene pipe with asmoother interior (a lower Mannings “n”), a smaller diameter pipe can often be selected in lieu of alternative pipe materials without adversely affecting capacities or modifying theslope of the line.The potential for settling is determine
44、d by the specific gravity and diameter of the particle and flow velocity. The formula for self-cleansing velocity is shown in Equation 5 or 5(a) for metric units.Equation 51VSC= 1.486R1/6B(sg - 1)Dg1/2nWhere:VSC= minimum self-cleansing velocity (fps)B = constant equal to 0.04 for clean granular part
45、icles or0.8 for cohesive material (unitless)sg = specific gravity of the soil particle (unitless)Dg = particle diameter (in)Equation 5(a)VSC= R1/6B (sg-1)Dg1/2nWhere:VSC= minimum self-cleansing velocity in a full-flow condition (m/s)R = hydraulic radius (m)B = constant equal to 0.04 for clean granul
46、ar particles or 0.8 for cohesive material, unitless12Self-Cleansing Velocitiessg = specific gravity of the soil particleDg = particle diameter (m)Soil types vary widely across the nation, as well as within states and counties. Separate calculations in each specific installation may prove impractical
47、, so an optimum self-cleansingvelocity for storm sewers is usually accepted to be 3 fps (1m/s).2In some specialized installations where sediment is a known problem, it may be wise to perform a soil analysis prior to final drainage design to determine the parameters necessaryfor Equation 5 or 5(a). B
48、y doing so, much off the guesswork is eliminated and sedimentationis kept to a minimum. In each design, a final check should be performed to compare theexpected velocity with the self-cleansing velocity. The actual effluent velocity can be calculated using Equation 6 or Equation 6(a) for metric unit
49、s.Equation 6V = 1.486R2/3 S1/2nEquation 6(a)V = R2/3 S1/2nDetermining actual effluent velocity can be greatly simplified through use of a chart, as shown in Figure 3, for partially full pipe flows. Proper use of this chart is demonstrated in Example 2. The design velocity for storm sewer applications should be a minimum of 3 fps (1m/s) or the value calculated through Equation 5 or Equation 5(a) for metric units.Figure 3: Determining Actual Effluent Velocity13Vfull,Qfull,Afull,RfullV Q A and RHydraulic elements in term
